pub fn new_birthday_probability(n: u32) -> f64 {
    const DAYS_IN_YEAR: u32 = 365;
    let mut unique_prob = 1.0;
 
    for i in 1..n {
        unique_prob *= (DAYS_IN_YEAR as f64 - i as f64) / DAYS_IN_YEAR as f64;
    }

    let at_least_one_collision_prob = 1.0 - unique_prob;

    (at_least_one_collision_prob * 10000.0).round() / 10000.0
}
